I was going to ask about a lens cap but I see it doesn't have one built-in. Do you see anything on the screen or view finder while you are recording or is it the screen and view finder blank only during playback? Link to manual: http/gdlp01.c-wss.com/gds/9/0900000699/01/ZR7065IM-EN.pdf - skip to troubleshooting section.
It could be the video heads are dirty and need cleaning. You could try a mini dv head cleaning tape like this one - http/www.amazon.com/Sony-DVM12CLD-DVC-Cleaning-Tape/dp/B0000632H7
OR try the method suggested in this video: http/www.youtube.com/watch?v=KUp1teer9jI
If you choose the cleaning tape method you need to follow the directions carefully as the cleaning tape is quite abrasive and can cause damage if not used properly. If you choose the Q-tip and alcohol method you use the Q-tips with the foam ends and not the cotton ends as the cotton will leave lint behind. Another method suggested you take a new tape and put it in the camcorder and run it for about a minute without rewinding the tape as it was suggested there would be debris on the tape. This is the least expensive and probably the safest method. You should be cautious with whatever method you choose as the video heads are quite delicate. The most expensive and maybe the best solution is to take it to a professional for cleaning. The downside of that solution is that it may end up costing more than a new camcorder.